VORTIME. The examiners have to be attached to a FSDO to conduct the check rides. I have done some FAA teaching in the UK and we had two options for check rides - this was over a year ago now so individual arranrgemants might have changed however we could either:
1. Use a Frankfurt based examiner examiner which meant either the student and aircraft going to Frankfurt or footing a heafty expenses bill.
2. Use a Saudi airline captain who flew into the UK and held an FAA examiner rating. Again expenses were involved and for reasons I won't go into here I personally didn't like the manner in which the tests were conducted.
There are several FAA instructors in the UK who may be conducting Flight Reviews and Instrument Proficiency checks but they are not examiners.
Yes there is definitely a market for FAA training in the UK principally for those who are considering buying private aircraft to be kept on the N register but if you are doing the training on a G reg aircraft you need the appropriate JAA licence/ratings. If however you have access to an N reg then things should be more straight forward. In this case I think you would also be okay to authorise solo students. I will stress however that I was really only involved in IR training and flight reviews so I never actually verified this point.